Volume 123, Number 3, August 2018
|Number of page(s)||6|
|Published online||24 August 2018|
Validity and failure of the Boltzmann weight
1 Centro Brasileiro de Pesquisas Físicas - Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
2 Departamento de Matemática Aplicada a la Ingeniería Aeroespacial, Universidad Politécnica de Madrid Plaza Cardenal Cisneros s/n, 28040 Madrid, Spain
3 National Institute of Science and Technology for Complex Systems - Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
4 Santa Fe Institute - 1399 Hyde Park Road, Santa Fe, 87501 NM, United States
5 Complexity Science Hub Vienna - Josefstädter Strasse 39, 1080 Vienna, Austria
Received: 11 April 2018
Accepted: 2 August 2018
The dynamics and thermostatistics of a classical inertial XY model, characterized by long-range interactions, are investigated on d-dimensional lattices (d = 1, 2, and 3), through molecular dynamics. The interactions between rotators decay with the distance rij like , where α → ∞ and respectively correspond to the nearest-neighbor and infinite-range interactions. We verify that the momenta probability distributions are Maxwellians in the short-range regime, whereas q-Gaussians emerge in the long-range regime. Moreover, in this latter regime, the individual energy probability distributions are characterized by long tails, corresponding to q-exponential functions. The present investigation strongly indicates that, in the long-range regime, central properties fall out of the scope of Boltzmann-Gibbs statistical mechanics, depending on d and α through the ratio .
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.40.Fb – Random walks and Levy flights / 05.70.Ce – Thermodynamic functions and equations of state
© EPLA, 2018
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